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Chapter 7: Problem 350

In the following exercises, find the additive inverse. $$ -32 $$

Short Answer

Expert verified
The additive inverse of -32 is 32.

Step by step solution

01

Understand the Additive Inverse

The additive inverse of a number is what you add to that number to get zero. For any given number 'a', its additive inverse is '-a'.
02

Apply the Definition

To find the additive inverse of -32, we add the opposite of -32. The opposite of -32 is 32.
03

Verify the Solution

Verify by adding the original number and its additive inverse: -32 + 32 = 0. Since this sum equals zero, 32 is indeed the additive inverse of -32.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

headline of the respective core concept
First, let's delve into understanding prealgebra. Prealgebra serves as the foundation for all future math courses. It involves basic arithmetic operations like addition, subtraction, multiplication, and division. It also introduces more complex concepts such as fractions, decimals, percents, and, importantly, negative numbers.
Understanding negative numbers is critical because they often come up in real-world situations. For example, temperatures below freezing are negative, as are bank account overdrafts. Grasping these concepts makes tackling prealgebra much easier as you'll be more comfortable with various scenarios that involve negative values.
headline of the respective core concept
Now, let's move on to opposite numbers. Every positive number has a negative counterpart, which is its opposite number. For example, the opposite of 5 is -5. Opposite numbers are also known as additive inverses. When you add a number and its opposite, the result is zero.
This property is very useful in solving equations and balancing accounts. Think of moving back and forth on a number line; if you move three steps forward and then three steps back, you end up where you started. This is a key concept in understanding how opposite numbers work.
headline of the respective core concept
Finally, we tie it all together with basic arithmetic. Basic arithmetic includes addition, subtraction, multiplication, and division. Knowing these operations is essential for finding additive inverses. For instance, in the exercise, we found that the additive inverse of -32 is 32. This is because when you add -32 and 32, you get zero.
If you're ever unsure, you can always double-check your work by performing the addition. If the sum is zero, you have found the correct additive inverse. This concept is straightforward but fundamental, providing a base for more advanced mathematical operations.

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